Basic Wireless Communication for Microcontrollers

Chapter 2 - Design Project 1: Crystal Radio Receiver

Radio Link Analysis

     The radio signal originates at the radio transmitter(figure 1). Here, an oscillator generates a constant amplitude AC voltage at the radio station's carrier frequency (590kHz, for example, for WARM 590 in Northeast Pennsylvania). This signal is then multiplied by the audio signal, creating an Amplitude Modulated (AM) radio signal, where the carrier amplitude varies according to the instantaneous audio voltage at each point in time. This signal, which is an electrical current, is amplified to a much greater power (typically a few thousand watts) and applied to an antenna. The result is that power is radiated out in all directions. When dealing with any communications system, there is some minimum power which the receiver must get in order to yield a usable signal. In a crystal receiver, this is determined by how much power the ear must receive in order to hear the station. In receivers with gain (powered receivers), it is ultimately determined by the noise level in the receiver, which is the combination of internal receiver noise and external noise and interference. Let's call this minimum detectible signal Pmin, measured in Watts.

Figure 1 - An ultra-simple AM radio transmitter site, similar (in concept) to typical AM broadcast stations.

Antenna Pattern and Effective Area

     Transmitting antennas do not radiate equally in all directions, but instead prefer certain angles. This can be described by an antenna pattern, as shown in figure 2. Usually, antennas will try to concentrate all their power into a narrow beam (beam antenas) or in all directions in a certain plane (omnidirectional antennas). Both types of pattern are shown in figure 2. This can be accounted for by determining the direction between the transmitter and receiver, and reading the gain off the plot of antenna pattern. The gain is the amount of power sent out in that direction relative to the amount which would be radiated in that direction by an isotropic antenna. Of course, the total power radiated by the theoretical, isotropic antenna and the real antenna are equal, and gain does not imply more power out than goes into the antenna. It is simply a way of taking into account the fact that more radiation goes out in certain directions than in others.
     Receiving antennas also exhibit directivity, and the best way to take that into account is to consider the effective area of the antenna to vary with angle. Once again, you can determine the direction between receiver and transmitter and read off the gain from the receiving antenna pattern plot. Then, you can use the equation Aeff=Gain*((lambda^2)/(4*pi)) to obtain the effective area for that direction. Notice that longer wavelengths also contribute to a greater effective area and that antennas with the same pattern will have larger effective areas for longer wavelengths. In a few cases, this can be an advantage to using longer wavelengths, but one must also take into account the ambient noise levels at the longer wavelenth, as well as the greater antenna size required, especially for directive antennas.

Figure 2 - Two examples to illustrate the concept of antenna pattern. The parabolic dish antenna forms a narrow beam, the same in the horizontal plane (azimuth) as in the vertical plane (altitude). The two pattern diagrams describe the gain (in dB) versus azimuth angle or altitude angle. The second example, a vertical monopole antenna radiates into an expaning "disk", which is omnidirectional in the horizontal plane but quite directional in the vertical plane. Try visualizing the 3D patterns of both antennas in your mind.

The Link Equation

     Once you know both the transmitting antenna gain and the receiving antenna's effective area, you can determine how much power the receiver gets for a given transmitted power. The power flux (power per area) at the receiving antenna's location is: [P]=Ptrans*Gain/(4*pi*r^2), where [P] is in Watts/meter^2 and r is in meters. If this is then multiplied by the Aeff for the receiving antenna, we get Prec, or Power received. So, the full equation is: Prec=Ptrans*Gain*Aeff/(4*pi*r^2).
     You must remember that this assumes no losses in either the transmitting or receiving antennas. You must reduce Ptrans according to the losses at the transmitter, and Prec should be multiplied by the efficiency of the receiving antenna system. Keep in mind, also, that this link equation only holds true in free space using line-of-sight propagation. If you are working indoors or in a city with many buildings, over distances where the curvature of the earth becomes important (which depends on antenna height), at frequencies where ground-wave or skip propagation is significant, or in an area with varied terrain including valleys, hills, or mountains, the results of this equation will be invalid. For simple RF links using microcontrollers indoors, it is probably best to just assume that the actual range will be about 5 times less than that predicted by this equation and then just test to see what the true range is.

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